The influence of substrate stiffness on interfacial stresses for adhesive microfibrils

Abstract

Bioinspired microfibrillar surfaces adhere by exploiting the presence of intermolecular forces at the contact interface. Experimental work has shown that compliant mushroom shaped fibrils can facilitate optimal adhesion across a range of substrates. This work evaluates numerically how fibril contact tip shape and the degree of elastic mismatch at the fibril-substrate interface influence adhesion. In a finite element simulation of fibrils subject to a remote stress, the interfacial stress distributions that define the detachment behaviour are computed for a range of fibril cap diameters, thicknesses, and substrate stiffnesses. Depending on the substrate stiffness, there is a singular stress field present at the edge of contact for smaller mushroom cap and straight punch fibrils while the stress at the corner for larger mushroom fibrils tends to zero. This variation in fibril-substrate interfacial stress has implications for the most probable defect type to initiate detachment and the stability of this crack growth. For fibrils within this corner singularity regime, the adhesion strength of a patch of fibrils is determined using interfacial fracture mechanics. The simulations are compared with experimental data of pull-off strengths and the biomedical applications of adhesive microfibrillar patches are considered.